Fetching the paper…
Reading the bibliography…
We provide a general framework to construct finite dimensional approximations of the space of convex functions, which also applies to the space of c-convex functions and to the space of support functions of convex bodies.
E. Meissner, Über Punktmengen konstanter Breite: Drei Gipsmodelle von Flächen konstanter Breite , Zeitschrift der Mathematik und Physik 60
1912
Earlier work this paper cites.
R. Schneider, Convex bodies: the brunn-minkowski theory , Cambridge Univ Prss, 1993
1993
Earlier work this paper cites.
B. Jüttler, Surface fitting using convex tensor-product splines , J. Comput. Appl. Math. 84
1997
Earlier work this paper cites.
Richard Jordan, David Kinderlehrer, and Felix Otto, The variational formulation of the fokker–planck equation , SIAM journal on mathematical analysis 29
1998
Earlier work this paper cites.
Jean-Charles Rochet and Philippe Choné, Ironing, sweeping, and multidimensional screening , Econometrica (1998), 783–826
1998
Earlier work this paper cites.
Guillaume Carlier, Thomas Lachand-Robert, and Bertrand Maury, A numerical approach to variational problems subject to convexity constraint , Numerische Mathematik 88
2001
Earlier work this paper cites.
Philippe Choné and Hervé VJ Le Meur, Non-convergence result for conformal approximation of variational problems subject to a convexity constraint , Numer. Funct. Anal. Optim. 5-6
2001
Earlier work this paper cites.
Thomas Lachand-Robert and Édouard Oudet, Minimizing within convex bodies using a convex hull method , SIAM Journal on Optimization 16
2005
Earlier work this paper cites.
by same author, Bodies of constant width in arbitrary dimension , Mathematische Nachrichten 280
2007
Cited alongside, same era.
Alejandro M Manelli and Daniel R Vincent, Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly , Journal of Economic Theory 137
2007
Cited alongside, same era.
V. Oliker, Embedding 𝒮 n \mathcal{S}^{n} into ℝ n + 1 \mathbb{R}^{n+1} with given integral Gauss curvature and optimal mass transport on 𝒮 n \mathcal{S}^{n} , Advances in Mathematics 213
2007
Cited alongside, same era.
Néstor E Aguilera and Pedro Morin, Approximating optimization problems over convex functions , Numerische Mathematik 111
2008
Cited alongside, same era.
J. Bertrand, Prescription of Gauss curvature using optimal mass transport , Preprint, 2010
2010
Cited alongside, same era.
Alessio Figalli, Young-Heon Kim, and Robert J McCann, When is multidimensional screening a convex program? , Journal of Economic Theory 146
2011
Later among the works it cites.
Bernd Kawohl and Christof Weber, Meissner’s mysterious bodies , Math. Intell. 33
2011
Later among the works it cites.
HaiLin Jin and Qi Guo, Asymmetry of convex bodies of constant width , Discrete & Computational Geometry 47
2012
Later among the works it cites.
Adam M Oberman, A numerical method for variational problems with convexity constraints , SIAM Journal on Scientific Computing 35
2013
Later among the works it cites.
Édouard Oudet, Shape optimization under width constraint , Disc. Comput. Geom. 49
2013
Later among the works it cites.
alphaXiv searches the wider corpus for related work and actual follow-ups.
alphaXiv is searching for related work…
Ivar Ekeland and Santiago Moreno-Bromberg, An algorithm for computing solutions of variational problems with global convexity constraints , Numerische Mathematik 115
2010
Cited alongside, same era.
Mary C Meyer, An algorithm for quadratic programming with applications in statistics , Tech. report, Technical Report, Colorado State University, 2010
2010
Cited alongside, same era.
Heinz H Bauschke, Regina S Burachik, Patrick L Combettes, Veit Elser, D Russell Luke, and Henry Wolkowicz, Fixed-point algorithms for inverse problems in science and engineering , (2011)
2011
Cited alongside, same era.
2013
Later among the works it cites.